Magnetic Particle Imaging (MPI) is a new tomographic imaging technique that maps the spatial distribution of iron oxide magnetic nanoparticles (MNPs) in real time and with spatial resolution that is on par or better than other biomedical imaging techniques. Because iron oxide MNPs are nontoxic, MPI is a safe imaging alternative for Chronic Kidney Disease (CKD) patients and due to its sensitivity it is suitable for angiography, cell tracking, cancer imaging, inflammation imaging, imaging major organs, and imaging of coronary arteries. Recently attention has shifted towards development of MNPs with ideal MPI signal characteristics. Unfortunately, these efforts are hampered by a lack of theories that predict the MPI signal due to MNP tracers, taking into account the finite relaxation dynamics of MNPs in time-varying magnetic fields typical of MPI. Because of this, most prior work on development of MNP MPI tracers has been limited to trial-and-error characterization of synthesized particles, without a theory guiding their rational design. What is needed is a solid theoretical foundation that will allow rational design of future generations of MNP MPI tracers and tuning of MPI magnetic field conditions to yield optimal image contrast and resolution. The proposed research will develop a theoretical foundation relating MNP properties (e.g., core size, hydrodynamic diameter, domain magnetization, magnetic anisotropy, particle-particle interactions, etc.) and MPI magnetic field conditions (strength of bias and excitation field, magnetic field gradient strength, scan rate, etc.) to the MPI signal strength and resolution. The proposed approach is unique and distinct from other work because we will develop stochastic computer simulation models of the response of MNPs to the magnetic fields typical of MPI, taking into account nanoparticle translation, physical rotation, internal dipole rotation, and particle-particle magnetic interactions. These models will enable systematic study of the large parameter space of particle properties and magnetic field conditions typical of MPI. The proposed work is significant because it will provide a much-needed theoretical understanding of the relation- ship between particle properties, MPI magnetic field conditions, and MPI signal strength and resolution. The proposed work is also significant because it will yield rules for the rational design of MNP MPI tracers with optimal signal strength and resolution and could also suggest novel applications of MPI beyond imaging of MNP tracer location and motion. The proposed work is innovative because it will yield this theoretical foundation through development of computer simulation platforms to model the response of MNPs to the magnetic fields generated in MPI through a combination of Brownian dynamics simulations of particle translation and rotation and the Landau-Lifshitz-Gilbert equation describing internal magnetic dipole rotation, an approach that is currently unexplored. The proposed work is also innovative because these computer simulation platforms will be used to explore the dependence of the MPI signal on MNP properties and MPI magnetic field conditions, yielding design rules to guide development of future generations of MPI tracers and MPI applications.